The value of escape velocity \( v_e \) for a planet depends on:
Show Hint
- the mass of the body thrown from the planet
- the direction of projection of the body
- the angle of projection
- only on the mass of the planet
- its mass \( M \), density \( \rho \), and radius of the planet
The Correct Option is
Solution and Explanation
Step 1: The escape velocity \( v_e \) is the minimum velocity required for an object to escape the gravitational pull of the planet.
The formula for escape velocity is: \[ v_e = \sqrt{\frac{2GM}{R}} \] where: - \( G \) is the gravitational constant,
- \( M \) is the mass of the planet,
- \( R \) is the radius of the planet.
Step 2: The escape velocity does not depend on the mass of the object being thrown, but depends on the mass \( M \) and radius \( R \) of the planet. Thus, the correct answer is that escape velocity depends on the mass, density, and radius of the planet.
Top KEAM Physics Questions
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- Two capillary tubes A and B of diameter $1\, mm$ and $2\, mm$ respectively are dipped vertically in a liquid. If the capillary rise in A is 6 cm, then the capillary rise in B is
- In the circuit given in figure, 1 and 2 are ammeters. Just after key K is pressed to complete the circuit, the reading will be
- A plate has a length $ 5\pm 0.1\text{ }cm $ and breadth $ 2\pm 0.01\text{ }cm $ . Then the area of the plate is:
Top KEAM Drift Velocity Questions
- The magnitude of tfie drift velocity per unit electric field is defined as
In the travelling plane wave equation given by \( y = A \sin \omega \left( \frac{x}{v} - t \right) \), where \( \omega \) is the angular velocity and \( v \) is the linear velocity.
The dimension of \( \omega t \) is:- A boy sitting in a bus moving at a constant velocity throws a ball vertically up in the air. The ball will fall:
- A machine gun fires a bullet of mass 25 g with a velocity of 1000 ms\(^{-1}\). If the man holding the gun can exert a maximum force of 100 N on the gun, the maximum number of bullets that he can fire per second is:
- When a vehicle moving with kinetic energy \( K \) is stopped in a distance \( d \) by applying a stopping force \( F \), the relation between \( F \) and \( K \) is given by:
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$